#
Folds
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}

The accumulate procedure is also known as fold-right, because it combines the first element of the sequence with the result of combining all the elements to the right. There is also a fold-left, which is similar to fold-right, except that it combines elements working in the opposite direction:

```
(define (fold-left op initial sequence)
(define (iter result rest)
(if (null? rest)
result
(iter (op result (car rest))
(cdr rest))))
(iter initial sequence))
```

What are the values of

```
(fold-right / 1 (list 1 2 3))
(fold-left / 1 (list 1 2 3))
(fold-right list nil (list 1 2 3))
(fold-left list nil (list 1 2 3))
```

Give a property that op should satisfy to guarantee that fold-right and fold-left will produce the same values for any sequence.

```
(define example (list 1 2 3))
(check-equal? (fold-right / 1 example) 3/2)
(check-equal? (fold-left / 1 example) 1/6)
(check-equal? (fold-right list '() example) '(1 (2 (3 ()))))
(check-equal? (fold-left list '() example) '(((() 1) 2) 3))
(check-equal? (fold-right + 0 example) (fold-left + 0 example))
(check-equal? (fold-right * 1 example) (fold-left * 1 example))
```